Raptor Code Designs for Finite Lengths and Practical Settings

In this dissertation we present new methods for designing efficient Raptor codes in finite and practical block lengths. First we propose an extension of Raptor codes which keeps all the desirable properties, including the linear complexity of encoding and decoding per information bit, and improves the performance in terms of the reception rate. Our simulations show a 10% reduction in the required overhead at the benchmark block length of 64,520 bits, and with the same complexity per information bit. Second, we consider the practical setting with short block lengths of 10 < k < 10. Based on a new vision of the inactivation decoding process, we set a new degree distribution design criterion for the Luby transform (LT) part of Raptor codes. A family of degree distributions that satisfy the new design criterion is analytically derived. The finite length performance of this family is investigated by using computer simulations and is shown to outperform the conventional design.